1. **State the problem:** We have an element with an initial mass of 420 grams that decays by 11.8% per minute. We want to find how much of the element remains after 16 minutes, rounded to the nearest tenth of a gram. 2. **Formula used:** The decay can be modeled by exponential decay formula: $$m = m_0 \times (1 - r)^t$$ where: - $m$ is the remaining mass after time $t$, - $m_0$ is the initial mass, - $r$ is the decay rate per unit time (as a decimal), - $t$ is the time elapsed. 3. **Apply the values:** - Initial mass $m_0 = 420$ grams - Decay rate $r = 11.8\% = 0.118$ - Time $t = 16$ minutes 4. **Calculate remaining mass:** $$m = 420 \times (1 - 0.118)^{16} = 420 \times (0.882)^{16}$$ 5. **Evaluate the power:** Calculate $(0.882)^{16}$: $$0.882^{16} \approx 0.1033$$ 6. **Multiply to find remaining mass:** $$m = 420 \times 0.1033 = 43.386$$ 7. **Round to nearest tenth:** $$m \approx 43.4 \text{ grams}$$ **Final answer:** After 16 minutes, approximately **43.4 grams** of the element remains.